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A317532 Regular triangle where T(n,k) is the number of multiset partitions of normal multisets of size n into k blocks, where a multiset is normal if it spans an initial interval of positive integers. 8
1, 2, 2, 4, 8, 4, 8, 34, 26, 8, 16, 124, 168, 76, 16, 32, 448, 962, 674, 208, 32, 64, 1568, 5224, 5344, 2392, 544, 64 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..28.

EXAMPLE

The T(3,2) = 8 multiset partitions:

  {{1},{1,1}}

  {{1},{2,2}}

  {{2},{1,2}}

  {{1},{1,2}}

  {{2},{1,1}}

  {{1},{2,3}}

  {{2},{1,3}}

  {{3},{1,2}}

Triangle begins:

    1

    2    2

    4    8    4

    8   34   26    8

   16  124  168   76   16

   32  448  962  674  208   32

MATHEMATICA

sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];

mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];

allnorm[n_]:=Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1];

Table[Length[Select[Join@@mps/@allnorm[n], Length[#]==k&]], {n, 7}, {k, n}]

CROSSREFS

Row sums are A255906.

Cf. A007716, A034691, A255397, A255903.

Sequence in context: A213418 A317517 A300182 * A222659 A116694 A220810

Adjacent sequences:  A317529 A317530 A317531 * A317533 A317534 A317535

KEYWORD

nonn,tabl,more

AUTHOR

Gus Wiseman, Jul 30 2018

STATUS

approved

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Last modified May 24 17:34 EDT 2019. Contains 323534 sequences. (Running on oeis4.)